Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
484 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22549762 | C2 | semidirect |
| 3. #22549746 | C2 | semidirect |
| 4. #22549742 | C2 | semidirect |
| 6. C4×C4⋊Dic127 | C2 | semidirect |
| 17. #117×C127 | C4 | semidirect |
| 89. C127 | #2314 | semidirect |
| 98. #117 | Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549769 | 2 |
| #22549762 | 2 |
| #22549746 | 2 |
| #22549742 | 2 |
| #22549736 | 2 |
| C4×C4⋊Dic127 | 2 |
| C2×#117×C127 | 2 |
| #2314 | 127 |